\newproblem{lay:2_3_13}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.3.13}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  An $m\times n$ upper triangular matrix is one whose entries below the main diagonal are 0's. When is a square upper triangular
	matrix invertible?
}{
  % Solution
	An upper triangular matrix is already in echelon form. It is row-equivalent to $I_n$, and hence invertible, if its diagonal elements are different from 0. If any of
	the diagonal entries is zero, then there would be free variables in the equation system $A\mathbf{x}=\mathbf{b}$ and the matrix would not be invertible.
}
\useproblem{lay:2_3_13}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
